# Design and implementation of dynamic logic gates and R-S flip-flop using quasiperiodically driven Murali-Lakshmanan-Chua circuit

## TL;DR

This paper demonstrates how a quasi-periodically driven Murali-Lakshmanan-Chua circuit can be used to implement dynamic logic gates and R-S flip-flops, with experimental, numerical, and analytical validation.

## Contribution

It introduces a novel method to realize multiple logic gates and flip-flops within a single circuit system using threshold-based signal propagation.

## Key findings

- Signal propagation occurs above a threshold amplitude.
- Single circuit can produce complementary logic gates simultaneously.
- Cross-coupled circuits mimic R-S flip-flop dynamics.

## Abstract

We report the propagation of a square wave signal in a quasi-periodically driven Murali-Lakshmanan-Chua (QPDMLC) circuit system. It is observed that signal propagation is possible only above a certain threshold strength of the square wave or digital signal and all the values above the threshold amplitude are termed as 'region of signal propagation'. Then, we extend this region of signal propagation to perform various logical operations like AND/NAND/OR/NOR and hence it is also designated as the 'region of logical operation'. Based on this region, we propose implementing the dynamic logic gates, namely AND/NAND/OR/NOR, which can be decided by the asymmetrical input square waves without altering the system parameters. Further, we show that a single QPDMLC system will produce simultaneously two outputs which are complementary to each other. As a result, a single QPDMLC system yields either AND as well as NAND or OR as well as NOR gates simultaneously. Then we combine the corresponding two QPDMLC systems in a cross-coupled way and report that its dynamics mimics that of fundamental R-S flip-flop circuit. All these phenomena have been explained with analytical solutions of the circuit equations characterizing the system and finally the results are compared with the corresponding numerical and experimental analysis.